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During a leap year does the Mitzvah to increase in joy apply in both months of Adar?
Some Poskim  write the Mitzvah to increase in joy only applies to Adar Sheiyni, however in Adar Rishon the Mitzvah does not apply. However the Rebbe, after analyzing this subject, concludes that the Mitzvah to increase in joy applies also in Adar Rishon. 
 Sheilas Yaavetz 88
 Likkutei Sichos 16 p. 344; Igros Kodesh Miluim [printed in Shulchan Menachem 3 p. 306]
 As we celebrate the birth of Moshe Rabbeinu in Adar Rishon and it is this matter which motivated the law of increasing in joy during Adar. [ibid] It is also supported from the fact the Mishneh in Megillah 6b does not list “joy” as one of the differences between Adar Rishon and Sheiyni.